Abstract
To locate the theory of Lie groups within mathematics, one can say that Lie groups are groups with some additional structure that permits us to apply analytic techniques such as differentiation in a group theoretic context.
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Notes
- 1.
The Norwegian mathematician Marius Sophus Lie (1842–1899) was the first to study differentiability properties of groups in a systematic way. In the 1890s, Sophus Lie developed his theory of differentiable groups (called continuous groups at a time when the concept of a topological space was not yet developed) to study symmetries of differential equations.
References
Adams, J. F., “Lectures on Exceptional Lie Groups.” Edited by Z. Mahmud and M. Mimura, Chicago Lectures in Mathematics, 1996
Goodman, R., and N. R. Wallach, “Symmetry, Representations, and Invariants,” Springer-Verlag, New York, 2009.
Knapp, A. W., “Lie groups beyond an introduction”. Second edition. Progress in mathematics 140, Birkhäuser, Boston, 2002
Wallach, N. R., “Real reductive groups I”, Academic Press, Boston, 1988
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Hilgert, J., Neeb, KH. (2012). Introduction. In: Structure and Geometry of Lie Groups. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84794-8_1
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DOI: https://doi.org/10.1007/978-0-387-84794-8_1
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